Hardy's inequalities for Hermite and Laguerre
expansions revisited

More by Yuichi KANJIN

Abstract

We show that Hardy's inequalities for Laguerre expansions hold
on the space $L^1(0,\infty)$ when the Laguerre parameters
$\alpha$ are positive, and we prove that although the
inequality holds on the real Hardy space $H^1(0,\infty)$ if
$\alpha= 0$, it does not hold on $L^1(0,\infty)$. Further,
Hardy's inequality for Hermite expansion is established on
$L^1(0,\infty)$.